The water molecules now in your body were once part of a molecular cloud. Only about onemillionth of the mass of a molecular cloud is in the form of water molecules, and the mass density of such a cloud is roughly 4.0×10−21 {\rm g}/{\rm cm}^{3}
Estimate the volume of a piece of molecular cloud that has the same amount of water as your body.
Assuming an average human body mass of 70 kg, the mass of water in the body is approximately 0.04 kg. Dividing this by the mass density of the molecular cloud (4.0×10−21 {\rm g}/{\rm cm}^{3}) gives a volume of 1.0×10−17 {\rm cm}^3.
To estimate the volume of a piece of molecular cloud that has the same amount of water as your body, we need to calculate the mass of water in your body. Let's break down the process step by step:
1. Calculate the mass of water in your body:
- According to the given information, only about onemillionth (1/1,000,000) of a molecular cloud's mass is in the form of water molecules.
- Assuming the mass of your body is "M," the mass of water in your body would be (1/1,000,000) * M.
2. Calculate the volume of the piece of cloud with the same amount of water:
- The mass density of the molecular cloud is given as 4.0×10^(-21) g/cm^3.
- We can use this information to find the volume of the cloud using the formula: Volume = Mass / Density.
Let's plug in the values and calculate:
Step 1: Calculate the mass of water in your body
- Let's assume your body mass, M, is 70 kg (you can adjust this value if needed).
- The mass of water in your body would be (1/1,000,000) * 70 kg.
Mass of water in your body = (1/1,000,000) * 70 kg
Step 2: Calculate the volume of the piece of cloud with the same amount of water
- The mass density of the cloud is 4.0×10^(-21) g/cm^3.
- Convert the mass of water in your body to grams (1 kg = 1000 g).
- Convert the mass density to the same units (1 g/cm^3 = 10^(-3) kg/m^3).
- Use the formula: Volume = Mass / Density.
Volume of the cloud = (Mass of water in your body in grams) / (Density of the cloud in kg/m^3)
By following these steps and plugging in the appropriate values, you can estimate the volume of the cloud that contains the same amount of water as your body.
To estimate the volume of a piece of molecular cloud that has the same amount of water as your body, we can use the following steps:
Step 1: Calculate the mass of water in your body.
Given that the average mass density of a molecular cloud is approximately 4.0×10^(-21) g/cm^3, and assuming your body mass is x grams, the mass of water in your body can be estimated as (1/1,000,000) * x grams.
Step 2: Convert the mass of water into volume.
We know that the density of water is 1 g/cm^3. To convert the mass of water into volume, we divide the mass by the density. Let's denote the volume as V.
V = (1/1,000,000) * x grams / 1 g/cm^3
Step 3: Simplify the volume equation.
Since 1 gram = 1 cm^3, we can simplify the equation to:
V = (1/1,000,000) * x cm^3
Therefore, the volume of a piece of molecular cloud that has the same amount of water as your body is estimated to be (1/1,000,000) times the volume of your body.